Oh man, if I was rich I would totally do stuff like this all the time. "You, random person off the street! I shall pay off all your debts and whisk you away to a year of luxury and ease for no reason!"
I feel like the people accusing the characters of being unrealistic are just jealous because they're not apparently wealthy enough to live out their insane pointless whims whenever they feel like it. Rich people in real life do weirder stuff than this every day.
The family's circumstances are weird, though it's not too difficult to imagine oddball but possible scenarios where Satoko would end up estranged from her father's new family but somehow living in another mansion on basically the same property.
This story could stand to be longer, to explore stuff like that and further develop Satoko and Yumi's characters. I particularly like Satoko, I wish we could see a lot more of her.